A Multi-Scale Time-Series Anomaly Detection Approach for Modeling the Time-Lagged Effects of Exogenous Variables

Abstract

Anomaly detection is essential for maintaining the stable operation of the Industrial Internet of Things (IIoT) and cyber-physical systems (CPS). Similar reliability requirements also arise in energy-aware computing environments, where workload variation, cooling policies, and resource-management decisions may affect system states with temporal delays. Existing methods usually focus on endogenous time-series variables, while delayed external effects are insufficiently explored. This paper proposes EMS-uDTWAD, a multi-scale uncertainty-aware dynamic time warping framework for anomaly detection with exogenous-context lag modeling. The proposed method constructs fine-grained and coarse-grained temporal windows to capture local structural deviations and segment-level temporal misalignment. A graph embedding module models fine-grained dependencies among variables, while a uDTW alignment module estimates uncertainty-aware alignment distances at the coarse-grained scale. The two branch scores are normalized and fused for final decision making. Experiments on a real-world system dataset with proxy exogenous-context inputs and a synthetic dataset with controlled delayed interactions show that EMS-uDTWAD outperforms representative baselines and remains robust under missing or disturbed auxiliary inputs.